While the above analysis does not constitute a comprehensive investigation into the eigenvalues and eigenvectors of \(W\) , this simplified derivation is, as shown in what follows, sufficient for our purposes.
For a detailed analysis, see [1]}.
To demonstrate the sufficiency of the above analysis, consider the following superposition of eigenvectors of \(W\) :
\(\frac{\left(1+i\hat{\lambda }_j\mu _j^-\right)\mathinner {|{v_j^+}\rangle } + \left(1+i\hat{\lambda }_j\mu _j^+\right)\mathinner {|{v_j^-}\rangle }}{\sqrt{2\left(1-\hat{\lambda }_j^2\right)}}.\) 
